Abstract:Two-dimensional crystal has been achieved and controlled with the aid of DC electric field applied between two electrodes at 5 millimeters separating distance between them. Sol-gel method has been used to prepared nanosilica particle which used in this work as well as TiO2 nanopaowder. The assembly of the silica particles is due to the interaction between the electrical force, the particles dipole, and the interaction between the particles themselves. When a DC voltage is applied, the particles accumulated and crystallized on the surface between the electrodes. The Light diffraction demonstrates that the hexagonal crystal is always oriented with one axis along the direction of the field. The particles disassemble when the field is

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fourth order by using the Lyapunov-Krasovskii functional approach; we obtain some conditions of instability of solution of such equation.

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fifth order with delay by using the Lyapunov-Krasovskii functional approach, we obtain some conditions of instability of solution of such equation.

Three-dimensional (3D) reconstruction from images is a most beneficial method of object regeneration by using a photo-realistic way that can be used in many fields. For industrial fields, it can be used to visualize the cracks within alloys or walls. In medical fields, it has been used as 3D scanner to reconstruct some human organs such as internal nose for plastic surgery or to reconstruct ear canal for fabricating a hearing aid device, and others. These applications need high accuracy details and measurement that represent the main issue which should be taken in consideration, also the other issues are cost, movability, and ease of use which should be taken into consideration. This work has presented an approach for design and construc

In this study, a cholera model with asymptomatic carriers was examined. A Holling type-II functional response function was used to describe disease transmission. For analyzing the dynamical behavior of cholera disease, a fractional-order model was developed. First, the positivity and boundedness of the system's solutions were established. The local stability of the equilibrium points was also analyzed. Second, a Lyapunov function was used to construct the global asymptotic stability of the system for both endemic and disease-free equilibrium points. Finally, numerical simulations and sensitivity analysis were carried out using matlab software to demonstrate the accuracy and validate the obtained results.

The aim of this paper is to present method for solving ordinary differential equations of eighth order with two point boundary conditions. We propose two-point osculatory interpolation to construct polynomial solution.

In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the met

In this paper, the dynamic behaviour of the stage-structure prey-predator fractional-order derivative system is considered and discussed. In this model, the Crowley–Martin functional response describes the interaction between mature preys with a predator.  e existence, uniqueness, non-negativity, and the boundedness of solutions are proved. All possible equilibrium points of this system are investigated.  e su‰cient conditions of local stability of equilibrium points for the considered system are determined. Finally, numerical simulation results are carried out to con‹rm the theoretical results.

A novel technique Sumudu transform Adomian decomposition method (STADM), is employed to handle some kinds of nonlinear time-fractional equations. We demonstrate that this method finds the solution without discretization or restrictive assumptions. This method is efficient, simple to implement, and produces good results. The fractional derivative is described in the Caputo sense. The solutions are obtained using STADM, and the results show that the suggested technique is valid and applicable and provides a more refined convergent series solution. The MATLAB software carried out all the computations and graphics. Moreover, a graphical representation was made for the solution of some examples. For integer and fractional order problems, solutio